Press CTRL+ALT+R to Rebake Textures if your skin/outfit remains fuzzy too long.
Currently, avatar baking is essentially driven from the viewer. This means that when a system layer outfit or item of clothing is changed (including alpha layers), the updates are applied locally in the user’s viewer. They are then uploaded to the server the user is connected to, which then passes the updates out to the other viewers connected to it, so that other users get to see the change as well.
This process has several points of potential failure: communications between the viewer and the server may be interrupted so the server doesn’t receive all the information pertaining to an outfit change, with the result that – for example – the user sees their avatar perfectly fine, but others see the avatar as blurred/grey. In some instances, the process can fail such that while the user sees their avatar wearing the desired outfit, other see the same avatar still wearing the “old” outfit.